Download GTU B.Tech 2020 Winter 4th Sem 3141005 Signal And Systems Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 4th Sem 3141005 Signal And Systems Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?IV (NEW) EXAMINATION ? WINTER 2020
Subject Code:3141005 Date:11/02/2021
Subject Name:Signal & Systems
Time:02:30 PM TO 04:30 PM Total Marks:56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS
Q.1 (a) Find even and odd parts of () = ().
03

(b) Check whether the following system is dynamic, causal, time invariant,
04
stable:
1
[] = {[] + [ - 1] + [ - 2]}
3

(c) Classify signals. Give examples of each.
07


Q.2 (a) Sketch the following waveform: () = ( + 1) - 2() - 2( - 1).
03

(b) Define energy and power. Hence, define energy signal and power signal.
04

(c) Evaluate continuous time (CT) convolution integral given as:
07
() = -2() ( + 2)







Q.3 (a) List out properties of convolution.
03

(b) Find the step response of the system whose impulse response is given as:
04
() = ( + 1) - ( - 1)

(c) Find the exponential Fourier series of Half wave rectifies sine wave shown
07
in figure:1.
Figure:1




Q.4 (a) Find the output of an LTI system with impulse response () = ( - 3) for
03
the input () = cos 4 + cos 7

(b) Calculate the convolution of [] and []:
04
[] = {1,1,0,1,1} [] = {1, -2, -3,4}

(c) Obtain the Fourier Transform of following signals:
07
1. () = cos 0 2. () = sin ()



Q.5 (a) State and prove frequency shifting property of Fourier Transform.
03

(b) Find the Fourier Transform of [] = -[- - 1] , where is real.
04

(c) Compute DFT of the following sequence [] = {0,1,2,3}
07



Q.6 (a) State and prove time scaling property of Fourier Transform.
03

(b) Bring out difference between DFT and Fourier Transform (FT).
04
1

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(c) Calculate the DFT of a sequence [] = {1,1,0,0} and check the validity of
07
DFT by calculating its IDFT.



Q.7 (a) Prove time shifting property of z- transform.
03

(b) What is ROC with respect to z- transform? What are its properties?
04

(c) Determine inverse z- transform of
07
1
() =
, || > 1
(1 + -1)(1 - -1)2



Q.8 (a) Prove differentiation in z-domain property of z- transform.
03
(b) Find the z- transform and ROC of the following sequence:
04
1
1 -
[] =
[ + 1] + 5 ( )
[] + 4[- - 1]
2
2
(c) Determine the sequence [] from following function:
07
1+-1
() =
Assume that [] is causal.
1--1+0.5-2

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2

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